Modern digital transmission is characterized by growing signaling rates requiring using the maximum possible channel bandwidth. There are numerous known approaches offering a tradeoff between robustness to channel's noise to power level, complexity and delay. Among undesired phenomena, which increase with the growing rate of transmission, is intersymbol interference (ISI). Intersymbol interference is a common practical impairment found in many transmission and storage systems, including voiceband modems, digital subscriber loop data transmission, storage disks, digital mobile radio channels, digital microwave channels, fiber-optic channels, etc. ISI is a form of distortion of a signal in which one symbol interferes with subsequent symbols having similar effect as noise, thus making the transmission less reliable. The problem of achieving reliable transmission over an ISI channel has been recognized in the art, and has been the subject of many studies over the past decades as, for example:
G. D. Forney, Jr. and G. Ungerboeck, “Modulation and coding for linear Gaussian channels,” IEEE Trans. Information Theory, vol. IT-44, pp. 2384-2415, October 1998.
Known solutions may be roughly divided into two classes: multi-carrier approaches and single-carrier approaches.
In multi-carrier transmission, the ISI channel is transformed into a set of parallel additive white Gaussian noise (AWGN) subchannels, each subchannel corresponding to a different frequency bin and experiencing a different SNR. This approach has the advantage that the subchannels are (virtually) ISI free, and thus the problems of equalization and decoding are decoupled. However, it has some drawbacks: the alphabet size of the transmitted symbols is considerably enlarged, which in turn makes the approach inapplicable to some media, such as, for example, magnetic recording channels. Furthermore, when channel state information (CSI) is available only at the receiver, bit allocation is precluded, and channel coding and decoding become more difficult, due to the variation of the SNR across subchannels.
Single-carrier approaches try to eliminate most of the ISI without severely increasing noise power, for example with the help of equalization attempting to remove the ISI prior to detection.
While many kinds of equalizers exist, they can be generally divided into 2 types:                1) Linear equalizers followed by symbol-by-symbol decision elements (such as Zero Forcing Equalizers, Minimum Mean Square Error (MMSE) Equalizers, etc.), and        2) Decision Feedback Aided Equalizers. These are non-linear equalizers, where the detector assumes that all previous data symbols were detected correctly and uses them in order to remove all ISI from past symbols, before deciding on the current symbol, using a symbol-by-symbol decision element.        
The first type usually cancels most of the ISI by roughly inverting the channel, but may suffer from poor performance due to noise enhancement that is a byproduct of the operation.
The second type is optimal in the sense of Minimum Mean Square Error (MMSE) before the symbol-by-symbol decision element, but has problems with combining with a forward error correcting code (FEC). These problems can be avoided if CSI is available at the transmitter, e.g. by Tomlinson-Harashima precoding which essentially moves the DFE to the transmitter, but is inapplicable if the transmitter has no knowledge of the channel.